This paper is a tutorial and a survey of analytical methods in the evaluation of data communication networks. The major mathematical methods are Markov chains applied to discrete time systems and queueing theory. Emphasis is placed on the applications of the mathematical tools. The discussion follows the framework of the layered architecture. In the section on data link control, rigorous as well as "engineering" approaches are highlighted. In this area, models of great accuracy have been developed. In the path-control or routing layer, the major model is provided by Kleinrock's delay analysis of packet networks. Finite buffer pools still pose many problems. The method of the homogeneous network is introduced, a method which reduces complexity originating from the network topology in favor of more realistic protocol features. This thought is expanded into the layer of end-to-end protocols where the tandem-queue model is introduced and its application to the flow-control problem discussed.

Performance evaluation of data communication systems

RECAL, a Recursion by Chain Algorithm for computing the mean performance measures of product-form multiple-chain closed queuing networks, is presented. It is based on a new recursive expression that relates the normalization constant of a network with r closed routing chains to those of a set of networks having (r - 1) chains. It relies on the artifice of breaking down each chain into constituent subchains that each have a population of one. The time and space requirements of the algorithm are shown to be polynomial in the number of chains. When the network contains many routing chains, the proposed algorithm is substantially more efficient than the convolution or mean value analysis algorithms. The algorithm, therefore, extends the range of queuing networks that can be analyzed efficiently by exact means.

RECAL—a new efficient algorithm for the exact analysis of multiple-chain closed queuing networks

In this paper, we develop two new general purpose recursive algorithms for the exact computation of blocking probabilities in multi-rate product-form circuit-switched networks with fixed routing. The first algorithm is a normalization constant approach based on the partition function of the state distribution. The second is a mean-value type of algorithm with a recursion cast in terms of blocking probabilities and conditional probabilities. The mean value recursion is derived from the normalization constant recursion. Both recursions are general purpose ones that do not depend on any specific network topology. The relative advantage of the mean-value algorithm is numerical stability, but this is obtained at the expense of an increase in computational costs.

Computational algorithms for blocking probabilities in circuit-switched networks

In this paper, we develop a new general-purpose recursive algorithm for the exact computation of blocking probabilities in multi-facility blocking models with some forms of state-dependent arrival rates. The recursion is cast in terms of the partition function of a product-form model. A dynamic scaling procedure is also proposed to avoid numerical overflow or underflow. The recursion is sufficiently general to be applied to a variety of different state-dependent arrival processes and service rate functions.

Exact computation of blocking probabilities in state-dependent multi-facility blocking models

Modeling and analysis of message switched computer-communication networks with multilevel flow control

This paper considers the problem of congestion in message-switched, or packet-switched, networks, which employ probabilistic routing schemes. A queueing model for the analysis of a local congestion control scheme is presented. Analytic study of the model shows that local congestion control with random routing is superior to similar control with deterministic routing for a particular example worked out here.

Local congestion control in computer-communication networks with random routing

In a recent paper a new recursive expression was obtained for the normalization constant of product-form multiple chain closed queueing networks This expression formed the basis of a new general purpose algorithm (named RECAL) for computing the mean performance measures This paper is concerned with the computational aspects of obtaining the normalization constant using the new recursive expression We present a computationally efficient formulation of the recursion and evaluate the computational complexity This new algorithm, for computing the normalization constant, is substantially more efficient than the convolution algorithm when there are many routing chains in the network The new algorithm therefore extends the range of queueing networks for which the normalization constant can be computed efficiently by exact means

A New Method For Computing The Normalization Constant Of Multiple-Chain Queueing Networks

A queueing model for the analysis of a local congestion control scheme is presented. Analytic study of the model shows that local congestion control witb random routing is superior to similar control with deterministic routing at least for the particular example considered here.

N.D. Georganas

Papers

Local congestion control in computer-communication networks with random routing

A New Method For Computing The Normalization Constant Of Multiple-Chain Queueing Networks

Application Note Local Congestion Control In Computercommunication Networks With Random Routing